Nonclassical symmetries of a class of Burgers' systems (Q990871)

The authors consider the nonclassical symmetries of the Burgers' systems \[ u_t= u_{xx}+ uu_x+ F(u,v)v_x,\qquad v_t= v_{xx}+vv_x+ G(u,v)u_x. \] This study was initiated by \textit{R. Cherniha} and \textit{M. Serov} [J. Math. Anal. Appl. 282, No.~1, 305--328 (2003; Zbl 1073.35192)] but with a restriction on the form of the nonclassical symmetry operator, namely they assume the form \[ \Gamma=\frac{\partial}{\partial t}+ X(t,x,u,v)\frac{\partial}{\partial x}+ U(u,v)\frac{\partial}{\partial u}+ V(u,v)\frac{\partial}{\partial v}. \] Here the authors review the restriction that \(U\) and \(V\) are independent on \(t\) and \(x\) and complete the analysis obtaining only symmetries that are truly nonclassical and inequivalent up to point equivalence transformations.